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A242452 Number of length n words on {1,2,3} with no more than one consecutive 1 and no more than two consecutive 2's and no more than three consecutive 3's.

%I A242452 #30 Aug 07 2015 16:52:49
%S A242452 1,3,8,21,54,140,362,937,2425,6275,16239,42024,108751,281430,728295,
%T A242452 1884709,4877320,12621710,32662931,84526348,218740428,566064618,
%U A242452 1464883079,3790878933,9810177543,25387142435,65697791726,170015189725,439971633412,1138574962157
%N A242452 Number of length n words on {1,2,3} with no more than one consecutive 1 and no more than two consecutive 2's and no more than three consecutive 3's.
%H A242452 Fung Lam, <a href="/A242452/b242452.txt">Table of n, a(n) for n = 0..1000</a>
%H A242452 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,4,3,2).
%F A242452 G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2)/(1 - x - 2*x^2 - 4*x^3 - 3*x^4 - 2*x^5).
%e A242452 a(3) = 21 because there are 27 length 3 words on {1,2,3} but we don't count: 111, 112, 113, 211, 222, 311.
%t A242452 nn=20;CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i])/.v[i]->(z-z^(i+1))/(1-z),{i,1,3}]),{z,0,nn}],z]
%t A242452 (* replacing the 3 in this code with a positive integer k will return the number of words on {1,2,...,k} with no more than one consecutive 1 and no more than two consecutive 2's and ... no more than k consecutive k's *)
%Y A242452 Cf. A000931 (binary words with at most one consecutive 1 and two consecutive 2's; offset=-8 for n>0).
%Y A242452 Cf. A007283 (ternary words with no consecutive like letters).
%Y A242452 Column k=3 of A242464.
%K A242452 nonn,easy
%O A242452 0,2
%A A242452 _Geoffrey Critzer_ and _Alois P. Heinz_, May 14 2014